1. Field of the Invention
The present invention relates to a spatial frequency reproducing apparatus and an optical distance measuring apparatus realizing, with a quite high resolution, measurement or observation of the profile of a surface condition or the surface condition of a cell or the like by irradiation of laser lights, and is preferable for an apparatus quantitatively and accurately performing observation or measurement of path difference information by improving the resolution of an optical apparatus such as a microscope and by accurately reproducing dropped spatial frequency information which is obtained with a lens.
2. Description of the Related Art
With a conventional optical microscope, it has not been possible to observe or measure an object under measurement at or below a diffraction limit. As a substitute for this, a probe microscope (STM, AFM, NFOS, or the like), a scanning electron microscope, and so on have been developed and used in many fields. The scanning electron microscope uses a very narrow beam as a scanning electron probe, and thus has a high resolution and a significantly large focal depth as compared to the optical microscope. However, for measuring an object under measurement with low electric conductivity such as a cell, it is necessary to coat platinum palladium or gold with good electric conductivity on a sample as the object under measurement. Accordingly, this often accompanies damage to a cell itself, and of course it has not been possible to observe and measure a live cell.
Further, the probe microscope is to measure the distance to the object under measurement by making a probe, which is disposed close to the object under measurement, further close to the object under measurement, and utilizing atomic force, tunnel current, light near field or the like. However, it is difficult to move the probe at high speed, handling is difficult because the distance to the object under measurement is quite close, and moreover a long time is needed for obtaining two-dimensional information.
On the other hand, a confocal microscope, a digital hologram microscope, and the like are known as a conventional means for detecting an optical path difference.
The former confocal microscope irradiates a spot light to an object under measurement, and moves the objective lens or the object under measurement so that the amount of light received on a photo detector disposed at a confocal position becomes the maximum for this spot light via a pin hole, to thereby obtain height information or path difference information of the object under measurement.
Further, the latter digital hologram microscope irradiates laser lights substantially in parallel to an object under measurement, gathers lights diffracted by the object under measurement through the objective lens, makes them interfere with a plane wave as a reference on an area sensor such as a CCD to generate a hologram, and analyzes interference fringes thereof by calculation to restore original wavefronts from the object under measurement, thereby obtaining path difference information.
However, in the former confocal microscope, basically, when there is a phase distribution within a spot, the beam is deformed, which results in erroneous information. In particular, for an object under measurement on which a wavefront changes in phase, like a refractive index change in a cell or the like, it is substantially equivalent to having an aberration in the optical system, and thus it must be said that reliability of the value thereof is poor. Further, it is necessary to move the objective lens and the object under measurement so that the received amount of light becomes maximum, and hence it is not real time.
In the latter digital hologram microscope, the diffracted lights are gathered through the objective lens, and their wavefronts are reproduced and taken as information. However, spatial frequencies which can be gathered with the objective lens are limited in cut-off frequency by NA of the objective lens, and at the same time, frequencies which can be obtained substantially linearly from DC to the cut-off frequency decreases gradually. What is called an MTF curve corresponds to this.
Therefore, the obtained wavefront information does not completely accurately reflect the spatial frequency information which the object under measurement has, and gives erroneous path difference information.
On the other hand, there is known a method which prepares a Fourier transform plane in part of an imaging optical system, disposing a spatial modulator of a phase type on this Fourier transform plane, and adds a phase modulation to a zero order diffracted light. This method images, by a CCD camera disposed on an imaging surface of a lens, four types of images in total in which phase differences of 90 degrees, 180 degrees, and 270 degrees differing by 90 degrees are generated between the zero order diffracted light and a first order diffracted light as described in Patent Document 2 and Non-Patent Documents 1, 2 below, and measures an optical distance from mutual calculations of these four types of images.
However, since any method based on this method images with a lens, it has MTF characteristics of the lens as described above, and thus a deficit in the amount of information occurs as a spatial frequency increase. Accordingly, it must be said that reliability of quantified information is poor by these methods.
Further, it has been practically impossible to generate a phase difference only in the zero order diffracted light. This is because the zero order diffracted light, which is a transmitted light without being modulated from a sample as an object under measurement, includes a first order diffracted light having a low frequency overlapped on a region of the zero order diffracted light, and the like, and the zero order diffracted light and the first order diffracted light cannot be substantially distinguished.
Moreover, upon obtaining four images with varied phases, it is necessary to switch modulation of the spatial light modulator, and thus the images obtained by the CCD camera provide information having time lags. Therefore, it is difficult to say that changes in processes which vary at a relatively high speed are reflected correctly.
On the other hand, in order to reduce the influence of the images becoming information having time lags as much as possible, it is conceivable to apply this method in a relatively narrow region in the vicinity of a peripheral portion of divergence of the zero order diffracted light. In this manner, there is a possibility of reducing frequency dependence of the spatial frequency and the influence of the first order diffracted light included in the zero order diffracted light. However, in this case, only lights in a quite narrow range can be obtained effectively, and thus the amount of light decreases largely, making it difficult to provide information having a good SN ratio.
Further, there is also known a demand to accurately analyze chemical changes of cells or the like by allowing cells or the like to emit a fluorescent light with a particular wavelength. However, in an imaging optical system, conventionally, there is an aperture limit by the objective lens. Thus, there is a limit in spatial frequency to be taken in, and at the same time, the contrast of the spatial frequency linearly decreases gradually as the frequency increases.
Accordingly, when emission of fluorescent light is performed in a structure part at a high frequency, the contrast thereof decreases, and it has been difficult to accurately perform concentration measurement or the like.
On the other hand, for measuring a distance accurately or for measuring or observing a micro object accurately, heterodyne interference methods are well known. Here, an optical heterodyne method using lights will be described, but it is also performed with the similar idea for other electromagnetic waves. This optical heterodyne method makes two laser lights with different frequencies interfere with each other to create a beat signal of the frequency difference, and detects a phase change of this beat signal with a resolution of about 1/500 of a wavelength. That is, with this optical heterodyne method, it is possible to measure the distance to an object under measurement while measuring a change in height direction of a surface, or to measure or observe an object under measurement itself.
Then, Japanese Patent Application Laid-open No. S59-214706 of Patent Document 1 below discloses a method to adjacently generate two beams composed of different frequencies by using an acoustic optical device, detect a phase change between these two beams, and obtain a surface profile by increasing the phase change cumulatively. However, this Patent Document 1 is to make two beams be close and slightly larger than a beam profile, detect an average phase difference in two beam profiles by heterodyne wave detection, and sequentially integrate the phase difference, so as to obtain concave and convex information.
Therefore, according to this Patent Document 1, it is possible to measure concave and convex information of an object under measurement which is assumed to be flat such as a semiconductor wafer, but it is not possible to extract information inside the beam profile. Accordingly, it is not possible to increase the resolution inside the beam profile, which is in a plane.
On the other hand, a method called DPC (Differential Phase Contrast) method has been conventionally known. This is a technique applied first to an electron microscope by Dekkers and de Lang, and is thereafter expanded to an optical microscope by Sheppard and Wilson and others. This DPC method obtains a differential signal of results of interference between a zero order diffracted light and a first order diffracted light detected by detectors, which are in a far field with respect to electromagnetic waves irradiated to a sample and disposed symmetrically with respect to an irradiation axis of the electromagnetic waves, to thereby obtain profile information of the sample. However, when a spatial frequency increases, this DPC method is not able to make these zero order diffracted light and first order diffracted light interfere, and as a result of that the spatial frequency cannot be reproduced, the measurement can no longer be performed in some cases.
That is, including general apparatuses and the like using electromagnetic waves, conventional imaging-type microscopes using electromagnetic waves cannot exceed a resolution which is the limit of the Abbe's theory. This limit is a result of a diffraction phenomenon which a wave has, and has been assumed as a theological limit that cannot be exceeded. Therefore, it has been difficult to overcome the substantial limit by wavelengths used in not only the optical microscopes but also the electron microscopes.
Further, in various conventional microscopes based on the imaging optical system, the obtainable spatial frequency is limited due to the aperture limit of lens, and at the same time, the contrast of a sample decreases gradually as the spatial frequency becomes high. Accordingly, it has been difficult to accurately obtain concentration information by path difference information such as phase information or fluorescent light emission.    Patent Document 1: Japanese Patent Application Laid-open No. S59-214706 (JP59214706(A))    Patent Document 2: Translated National Publication of Patent Application No. 2007-524075    Non-Patent Document 1: Opt. Lett. 29(21), 2503-2505 (2004)    Non-Patent Document 2: Opt. Exp. 19(2), 1016-1026 (2011)
As described above, in a conventional distance measurement apparatus using the heterodyne detection, it has not been possible to measure a distance with a resolution equal to or smaller than the wavelength of an electromagnetic wave to be given. Therefore, even when the irradiation area of the electromagnetic wave is decreased to be equal to or smaller than a wavelength, it has only been possible to calculate an average distance of an area to the extent equal to or larger than the wavelength.
Similarly, in a conventional optical detector using the heterodyne detection, a near-flat object such as a semiconductor wafer is a main target of measurement. Accordingly, to increase the resolution in a plane, it has been inevitable to use the near field of the electronic microscope, AFM (atomic force microscope), or the like.
However, regarding the electronic microscope, processing of a living organism, cell, or the like in particular is necessary, and thus live observation or measurement of a refractive-index distribution is not possible. On the other hand, the AFM has insufficient processing speed and hence is unable to see a change of state in real time. Thus, it is not suitable for observation of a living organism or cell, and meanwhile the probe needs to be close to the object under measurement, which causes poor usability.
Here, the OTF characteristics of an objective lens in a conventional microscope using an imaging optical system will be described below.
In the conventional microscope using an imaging optical system, the component of a first order diffracted light and the component of a zero order diffracted light of the spatial frequency of a target object, which is captured with the objective lens, interfere with each other to form an image. Accordingly, when the first order diffracted light is not incident on the aperture of the lens, the spatial frequency thereof would not be reproduced. On the other hand, the angle of diffraction of the first order diffracted light increases gradually as it varies from a low frequency to a high frequency, and hence the amount of the first order diffracted light inputted to the lens decreases gradually. As a result, the frequency whose first order diffracted light is not inputted is cut off, and the degree of modulation thereof gradually decreases in the course of variation from the low frequency to the high frequency.
The OTF characteristics of the objective lens are as described above. Therefore, in the imaging system, the first order diffracted light to be inputted to the objective lens is limited itself, and thus the resolution itself has a limit in relation with the spatial frequency of the object under measurement to be reproduced.
On the other hand, in an optical system which images using an objective lens like the aforementioned digital hologram microscope, at the time when being incident on the objective lens limited in size of aperture, the laser lights diffracted by the object under measurement are in a state that information of part of the spatial frequency which this laser light has is dropped. That is, as the spatial frequency increases, the spatial frequency inputted to the objective lens decreases gradually. Accordingly, the hologram created by making interference with the wavefront of reference does not reflect the original information which the object under measurement has. As a result, the path difference information reproduced by this calculation is utterly erroneous information particularly in an area where the spatial frequency is high.
The above qualitative explanation is quantified and described in detail below.
As in FIG. 29, it is assumed that a parallel luminous flux is incident on an objective lens 31 having an aperture radius a and a focal length f. Note that in FIG. 29, an irradiation optical axis is represented by an optical axis L0, and a tilted optical axis tilted by an angle Θ with respect to this optical axis L0 is represented by an optical axis L1. A microscope using normal imaging is a transmission type in which the luminous flux transmits a sample S as in FIG. 29, but it may be considered as a reflection type in which the luminous flux is returned by the sample S. Further, to make the equations simple, it is handled as a one-dimensional aperture.
Further, for simplicity, the sample S is assumed to be in the form of a sine wave with a height h and a pitch d. Specifically, an optical phase θ is represented by the following equation.θ=2π(h/λ)sin(2πx/d)  Equation (1)
The amplitude E of a light deflected from the sample S is given as a convolution of Fourier transform of Equation (1) and the aperture of the lens on a plane separated by the focal length f, and hence is represented as follows. However, the Bessel function which is Fourier transform of the phase of Equation (1) takes up to the positive and negative first order.
                                                        E              =                            ⁢                              ∫                                  (                                                                                                              J                          0                                                ⁡                                                  (                                                      2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                          h                              λ                                                                                )                                                                    ⁢                                              δ                        ⁡                                                  (                          X                          )                                                                                      +                                                                                            J                          1                                                ⁡                                                  (                                                      2                            ⁢                                                                                                                  ⁢                            π                            ⁢                                                          h                              λ                                                                                )                                                                    ⁢                                              (                                                                              δ                            ⁢                                                          (                                                              X                                -                                                                                                      λ                                    ⁢                                                                                                                                                  ⁢                                    f                                                                    ⅆ                                                                                            )                                                                                -                                                                                                                                                                                                                                                ⁢                                      δ                    ⁢                                          (                                              X                        +                                                                              λ                            ⁢                                                                                                                  ⁢                            f                                                    ⅆ                                                                    )                                                        )                                )                            ⁢                              rect                ⁡                                  (                                                            x                      -                      X                                                              2                      ⁢                                                                                          ⁢                      a                                                        )                                            ⁢                              ⅆ                X                                                                                        =                            ⁢                                                                                          J                      0                                        ⁡                                          (                                              2                        ⁢                                                                                                  ⁢                        π                        ⁢                                                  h                          λ                                                                    )                                                        ⁢                                      rect                    ⁡                                          (                                              x                                                  2                          ⁢                                                                                                          ⁢                          a                                                                    )                                                                      +                                                                                                      ⁢                                                                    J                    1                                    ⁡                                      (                                          2                      ⁢                                                                                          ⁢                      π                      ⁢                                              h                        λ                                                              )                                                  ⁢                                  (                                                            rect                      (                                                                        x                          -                                                                                    λ                              ⁢                                                                                                                          ⁢                              f                                                        d                                                                                                    2                          ⁢                                                                                                          ⁢                          a                                                                    )                                        -                                          rect                      (                                                                        x                          -                                                                                    λ                              ⁢                                                                                                                          ⁢                              f                                                        d                                                                                                    2                          ⁢                                                                                                          ⁢                          a                                                                    )                                                        )                                                                                        Equation        ⁢                                  ⁢                  (          2          )                    
Here, the Fourier transform of Equation (2) contributes to imaging.
Therefore, intensity I is as following Equation (3)
                    I        =                                            (                                                                    J                    0                                    ⁡                                      (                                          2                      ⁢                                                                                          ⁢                      π                      ⁢                                              h                        λ                                                              )                                                  *                a                *                sin                ⁢                                                                  ⁢                                  c                  ⁡                                      (                    ka                    )                                                              )                        2                    +                      2            *                                          (                                                      J                    1                                    *                                      (                                          2                      ⁢                                                                                          ⁢                      π                      ⁢                                              h                        λ                                                              )                                    *                                      (                                          a                      -                                                                        λ                          ⁢                                                                                                          ⁢                          f                                                                          2                          ⁢                                                                                                          ⁢                          d                                                                                      )                                    *                  sin                  ⁢                                                                          ⁢                                      c                    ⁡                                          (                                              k                        ⁡                                                  (                                                      a                            -                                                                                          λ                                ⁢                                                                                                                                  ⁢                                f                                                                                            2                                ⁢                                                                                                                                  ⁢                                d                                                                                                              )                                                                    )                                                                      )                            2                        *                          (                              4                ⁢                                                                  ⁢                                                      sin                    2                                    ⁡                                      (                                          2                      ⁢                                                                                          ⁢                      π                      ⁢                                              x                        d                                                              )                                                              )                                                          Equation        ⁢                                  ⁢                  (          3          )                    
What this equation means is that information of a pitch smaller than d=λf/2a=0.5λ/NA is dropped. This matches the beam diameter of a rectangular opening (the first dark ring radius w of sinc(ka)=0 satisfies ka=π, and thus w=0.5/NA). Further, this means that even when d>0.5/NA, the degree of modulation decreases as d becomes smaller. When the relation of this with the spatial frequency of 1/d and the degree of modulation is indicated, it is MTF. However, by just imaging phase information, image formation having contrast is not performed, and hence a means for making contrast by using an optical element or the like which causes a phase delay in a zero order diffracted light like a phase contrast microscope is necessary.
As described above, in the ordinary imaging optical system, the limit of the spatial frequency reproduced by NA of the objective lens 31 is inevitably d=λf/2a=0.5λ/NA, and any value smaller than this would not be reproduced in any way. Accompanying this, conventional optical microscopes including the digital hologram microscope which obtains information with an objective lens, it has not been possible to obtain accurate intensity information or path difference information.